Non-Convex Sparse Reinforcement Learning via Non-Monotone Inclusions

• URL: http://arxiv.org/abs/2607.04990v2
• Date: Tue, 07 Jul 2026 05:16:42 GMT
• Title: Non-Convex Sparse Reinforcement Learning via Non-Monotone Inclusions
• Abstract summary: This work delivers two key contributions one to efficient feature selection in reinforcement learning (RL) and the other to the theory of non-monotone inclusions.
• Score: 7.408148824204063
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work delivers two key contributions: one to efficient feature selection in reinforcement learning (RL), the other to the theory of non-monotone inclusions. On the RL side, the estimation bias inherent in conventional regularization schemes is addressed by augmenting classical least-squares temporal-difference (LSTD) policy evaluation with the sparsity-inducing, non-convex projected minimax concave (PMC) penalty. Because the PMC penalty is weakly convex, the resulting fixed-point problem is no longer monotone; instead, it falls under a broader class of non-monotone inclusions involving the sum of a monotone Lipschitz operator and a hypomonotone operator. On the theory side, novel convergence conditions are developed for the forward-reflected-backward splitting (FRBS) method applied to this broader class of non-monotone inclusion problems. Under mild conditions, Lyapunov stability and the existence of a limit point of the sequence of FRBS iterates are established; alternatively, under the weak Minty variational inequality assumption, exact convergence is guaranteed. Numerical tests on benchmark datasets show that the proposed FRBS iterates, applied to the non-convexly regularized LSTD problem, substantially outperform state-of-the-art feature-selection methods, especially when many noisy features are present.

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